Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
n = int(input())
n = 2 * n
up = int(math.sqrt(n))
n = n / 2
arr = [0] * (up + 1)
for i in range(0,(up + 1)):
    arr[i] = int((i * (i + 1)) / 2)
flag = 0
lo = 1
while lo <= up:
    if arr[lo] + arr[up] == n:
        flag = 1
        break
    elif arr[lo] + arr[up] < n:
        lo = lo + 1
    elif arr[lo] + arr[up] > n:
        up = up - 1
if(flag == 1):
    print("YES")
else:
    print("NO")